Page 425 - Bruce Ellig - The Complete Guide to Executive Compensation (2007)

Chapter 8. Long-Term Incentives 411

c Se q(T) Nd Xe r(T) Nd 2
1
c Call option value
S Stock price (current)
e 2.71828 (exponential constant)
q Expected dividend yield
T Time to expiration
N From standard normal distribution probability that
dx
random draw is less than dx
X Exercise or strike price of the option
r Risk-free rate of return expectation
Table 8-3. Black-Scholes formula for a call option

for a new method to determine the value of derivatives, (Fisher Black had died and was
therefore not eligible for the award), the formula is now known as the Black-Scholes-Merton
formula or, alternatively, Black-Scholes.
Other things being equal, the Black-Scholes model (and other pricing models) will place
a greater value on a higher-priced stock option. For example, a stock option priced at $81 a
share may be said to be worth $32.69. Because of a significant decline in the price of its stock
the following year, the company issues an option at $63 a share, which is given a valuation of
$22.32 a share. This is illustrated in Table 8-4. Is there anyone who does not believe the
$63 option is more valuable to the optionee than the $81 option? Yes—FAS 123R.

Last Year This Year
Term 10 years 10 years

Strike price $81.00 $63.00

Market price $81.00 $63.00
Volatility 26% 31%
Risk-free rate 6,526% 5,487%

Dividend yield 1.83% 2.7%

Valuation (per option) $32.69 $22.32
Table 8-4. Stock option valuation
Some have argued that option recipients place a much smaller value on the option than
does the Black-Scholes formula. A few have gone further, indicating that if the Black-Scholes
value is $33 on a $100 option, the more likely true value is a third ($11) or maybe half
($16.50) that amount. It could be argued, therefore, that options “cost” the company more
than the value assigned them by the optionee. In any event, is the option really a cost to the
company or a transfer of value from the shareholder? If it is a transfer, why should it be taken
as a charge to earnings as required by FAS 123R?